Measurements of the earth's gravitational acceleration, and measurements of differences in the earth's gravitational acceleration (gravity difference) between different depths in the earth or horizontal positions, can be useful in determining the bulk density (or specific gravity) of various earth formations, among other applications. More particularly, measurements of gravity difference between two positions or depths may be used to determine whether oil, water or gas primarily fills pore spaces in the earth formations at various depths and geographic locations in the earth.
Such measurements can also be useful in operations where a fluid, such as a gas, liquid, gel, or foam, is injected into a subterranean formation to enhance or promote the recovery of hydrocarbons with low mobility. To monitor the effectiveness of such treatments it is often desirable to detect at least the depth and/or the position of the fluid front as formed by the injected fluid.
As a practical matter, measuring physical properties of earth formations beneath the surface of the earth is typically performed by a process called “well logging”, wherein instruments having various sensors therein are lowered into a wellbore drilled through the earth. The instruments may be lowered into the wellbore and retrieved therefrom at the end of an armored electrical cable in a process known as “wireline” well logging. Alternative conveyance techniques as known in the art include lowering the instruments into the wellbore coupled to the end of a drill pipe, a production tubing or a coiled tubing. The drill pipe conveyance technique, in particular, is commonly referred to as “logging while drilling” when performed during the actual drilling of a wellbore. The well logging instruments, whether wireline or pipe conveyed, may include various devices to measure the earth's gravitational acceleration.
Several gravity measurement tools are commercially available or have been proposed in the prior art. One manufacturer of such tools is for example Lacoste & Romberg who offer a borehole gravity meter (BHGM) under the trade name “Micro-g system”.
Other gravity and gravity difference measuring instruments are for example described in U.S. Pat. Nos. 5,351,122 and 5,892,151 both issued to Niebauer et al. and 5,903,349 to Vohra et al. The known gravity tools according to the '151 patent include at least one, preferably several longitudinally spaced apart gravity sensors enclosed in an instrument housing. The gravity sensors are fiber optic interferometry devices, which measure a velocity of a free falling mass by determining, with respect to time, interference fringe frequency of a light beam split between a first path having a length corresponding to the position of the free falling mass, and a second “reference” (fixed length) path. The fringe frequency is related to the velocity of the free falling mass, which in turn can be correlated to earth's gravity by precise measurement of the mass's position and the time from the start of free fall. Measurement of gravity difference is performed by determining a difference in gravity measurements made between two of the individual gravity sensors positioned at locations vertically spaced apart.
Further instruments for gravity and gravity difference measuring are described in co-owned U.S. Pat. No. 6,671,057 issued to Orban including a gravity sensor with a first mass adapted to free fall when selectively released from an initial position. The mass has optical elements adapted to change the length of an optical path in response to movements of the mass. The sensor output is coupled to a beam splitter. One output of the splitter is coupled substantially optically directly to an interferometer. Another output of the splitter is coupled to the interferometer through an optical delay line. The frequency of an interference pattern is directly related to gravity at the mass. A second such mass having similar optics, optically coupled in series to the first mass and adapted to change the path length in opposed direction when selectively dropped to cause time coincident movement of the two masses, generates an interference pattern having frequency related to gravity difference. Further suitable gravity measuring instrument are known for example as U.S. Pat. No. 7,155,101 to Shah et al.
Methods of using such instruments are described for example in the above '057 patent and in the U.S. Pat. No. 7,069,780 to Ander, and by J. L. Hare et al. in: “The 4-D microgravity method for waterflood surveillance: A model study for the Prudhoe Bay reservoir, Alaska”, in Geophysics, Vol. 64, No. 1 (January-February 1999), p. 78-87. In the latter study, the gravity observations are inverted to determine the subterranean density distribution. The inversion used in this prior art is posed as a linear, underdetermined inverse problem with an infinite number of possible solutions. The densities range is subjected to a set of constraints resulting in a constrained, linear system which can be solved using least-square methods. The authors acknowledge that the model parameters determined using the least-square methods are not unique. In addition, the inverse gravity problem is stated to be fundamentally unstable and it is known that any solution based on an optimization approach involves high computational costs.
Given that gravimetric instruments and logging measurements are known per se, it is seen as an object of the present invention to provide new methods for making use of and evaluating gravity logging measurements to determine the depth and/or other geometrical properties of a gravitational anomaly in a subterranean formation. It is a particular object of the invention to provide such methods for monitoring changes in subterranean reservoirs fast and with limited computational costs.